Appendix A1: California State Standards2

Grades K-3 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 3)

Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:

2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).

2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).

2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.

2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

2.6 Identify common solid objects that are the components needed to make a more complex solid object.

Grades 4-5 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 5)

Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).

2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

Grades K-3 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 3)

Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:

2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).

2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).

2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.

2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

2.6 Identify common solid objects that are the components needed to make a more complex solid object.

Grades 4-5

Grade 4 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 3.0, grade 4)

Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:

3.2 Identify the radius and diameter of a circle.

3.3 Identify congruent figures.

3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.

3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

Grade 5 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 5)

Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).

2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.

2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

Grades K-3 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 1)

Students identify common geometric figures, classify them by common attributes, and describe their relative position or their location in space:

2.3 Give and follow directions about location.

2.4 Arrange and describe objects in space by proximity, position, and direction (e.g., near, far, below, above, up, down, behind, in front of, next to, left or right of).

Grades 4-5

Grade 4 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 4)

Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:

2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10points on the graph of the equation y=3x and connect them by using a straight line).

2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates.

2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates.

Grade 5 (Mathematics Content Standards for California Public Schools, Algebra and Functions, 1.0, grade 5)

Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:

1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.

Grades K-3 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 2.0, grade 3)

Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:

2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).

2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

Grades 4-5 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 3.0, grade 4)

Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:

3.4 Identify figures that have bilateral and rotational symmetry.

Grades K-3 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 1.0, grade 3)

Students choose and use appropriate units and measurement tools to quantify the properties of objects:

1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.

1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.

1.3 Find the perimeter of a polygon with integer sides.

1.4 Carry out simple unit conversions within a system of measurement (e.g., centimetersand meters, hour and minutes).

Grades 4-5 (Mathematics Content Standards for California Public Schools, Measurement and Geometry, 1.0, grade 5)

Students understand and compute the volumes and areas of simple objects:

1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram).

1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects.

1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter, cubic meter, cubic inch, cubic yard tocompute the volume of rectangular solids).

1.4 Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects (i.e., find the perimeter, area, volume).